WASHINGTON—House Republicans are considering a plan to include a duo of unrelated policy measures in a bill raising the federal borrowing limit, possibly as soon as the coming week.

While GOP leaders are still mulling their options, one strategy would be to affix two policy proposals to a debt-ceiling increase that would push any new fight into 2015. One measure would attach to the legislation a nine-month "doc fix," which would halt a Medicare payment reduction for doctors that is rooted in a 1997 budget law....